Displacement Vs Distance: 11 Complete Quick Facts


Distance and displacement are the two different physical quantities. In this article, we are going to know about Displacement Vs. Distance in detail.

The terms distance and displacement may sound similar, but they are different. Displacement measures the length of the linear course in which the body moves concerning direction. In comparison, distance is the total length of the route covered by a body irrespective of orientation.

Now let us see the different aspects of displacement v/s distance in detail.

Displacement v/s distance

Distance and displacement are two different physical quantities that have different natures. Let us know about it through the following table,

               Distance          Displacement
                             DefinitionThe definition of distance is the total measurable length of the path covered by an object between initial and final points during its motion.Displacement is the calculation of the straight course of the object when it is in motion. It is a term that focuses on the shortest and less length between starting and endpoints.
               Nature of QuantityIt is a physical scalar quantity.It is a physical vector quantity.
                           Components Only magnitudeBoth Direction and Magnitude.
                               ExplanationWhen a body travels, the distance measures the sum of all course lengths covered, not considering the direction of movement.When a body is in motion, the displacement is the calculation, as it measures the minimum size of the course covered, considering the direction of movement.
                 Dependency on time It does not depend on time.It is directly proportional to time and decreases with time.
                          SymbolIt is indicated by a symbol ‘d’It is indicated by a symbol ‘s.’
                          ComparisonDistance always has a higher value compared to displacement.Displacement will have a lower or sometimes equal value compared to distance.
              Direction It does not give information about direction of the path.Direction is necessary in finding displacement.
              Formula = d1 +  d2  = xf – xi           
                           Signs Distance is always positive and cannot have negative or zero values.Displacement can be positive, zero, and even negative, depending on the path.
                          ExampleThe total length of the curved path on which the vehicle moves. The shortest distance between home and neighbor shop.
Displacement Vs distance

These are some fundamental differences of displacement vs. distance.

Distance and displacement: Detailed Analysis

To understand the comparison of distance and displacement, we must know about scalars and vectors.

  • Distance is one of the examples of a scalar quantity. It is a physical quantity that deals with measuring the magnitude of length of the entire route on which a person, object, or animal moves.
  • Displacement is one of the examples of a vector quantity. It is a physical quantity that deals with the measure of the magnitude of route length and the direction of a body’s route.

To learn more about displacement Vs distance, check the following posts

  1. Is distance vector or scalar?
  2. Is displacement scalar or vector?

Nature of quantities of distance and displacement

There are two types of quantities based on their nature, i.e., a scalar and a vector quantity.

  • Scalars are physical quantities that measure the extent of the length, size, speed of the body, and distance, which is an actual example of a scalar.
  • Vectors are physical quantities that measure the extent of an amount length and deal with the direction of a route on which a body moves. Displacement is an actual example of a vector.

The distance and displacement belong to a different group of physical quantities.

Different cases based on the nature of distance and displacement

The distance can only be positive since it is a scalar. However, displacement is a vector and is seen in a coordinate system.

Case 1:

A person walking in the forward direction is positive.

Case 2:

A person walking in the backward direction is negative.

Case 3:

A person travels in all directions and comes back to the start point.

Therefore, scalars are always positive, and vectors can change their sign.

Mathematical expressions for distance and displacement

Both distance and displacement can be expressed in the form of mathematical formula to measure the length of the path.

Formula to calculate distance

The formula for distance used in physics to measure the path length is given as,

= d1 +  d2 

= Sum of total length of route

d1 = Distance covered in first interval.

d2 = Distance covered in second interval.

Formula to calculate displacement

The formula for displacement used in physics to measure the linear path length is given as,

= xf     – xi 

= Difference between start and an endpoint

xi = length of the body towards an initial point.

xf = length of the body towards the end. 

Apart from these basic formulas, there are other formulas used to calculate path length.

Solved problems on Distance and Displacement

These are some numericals on displacement Vs distance.

Problem 1

Kaveri travels 400 miles to the east but then goes back to the west for 205 miles to meet her colleague. What is Kaveri’s total displacement?

Answer: Kaveri’s starting position is given as Xi = 0.

Her final position is taken as

where Xf is the distance traveled east minus the distance west.

To Calculate displacement, i.e., D

d = ΔX = (Xf – Xi)

d = (400 – 205) – 0

d = 195 miles.

Therefore, the total displacement is 195 miles.

Problem 2

A person moves along the tiles grid through points P, Q, R, T, U, and V, as shown below. The side of each square grid measures 0.4 km.

a) Calculate the total distance covered by the moving person.

b) Find the magnitude of the displacement of the person.

Displacement Vs distance

Solution:

a) The total distance covered by the person can be calculated as follows:

PQ + QR + RT + TU + UV

0.4 + 0.4 + 0.4 + 0.8 + 0.8 = 2.8 km

The total distance covered by the person is 2.1 km.

b) To calculate the magnitude of a person from the start point P to endpoint V. Therefore, the total displacement is the length between P to V. It can be calculated with the help of the Pythagoras theorem.

Apply the Pythagoras formula, we get

(PV)2 = (PU)2 + (UV)2

Substituting the values, we get

(PV)2 = (0.4 x 3)2 + (0.4 x 2)2

(PV)2 = 1.44 + 0.64

(PV)2 = 2.08

    PV =

PV = 1.44 Km

The numerical value of displacement is 1.44 Km.

Real-life Examples of distance and displacement

There are certain circumstances in daily life where we encounter distance and displacement.

  • A dog roams in all directions and comes back to its rest point. Here the total length of the route is distance, and length along a specific order is displacement.
  • A boy goes to a store by taking the most extended length of the path; it is his distance, and while coming back, he takes the shortest route length; it is his displacement.

These are some real-life examples of displacement and distance.

Distance and Displacement: Similarities

Even though distance and displacement belong to two different quantities, some similarities should be known,

  • The international system of units for both distance and displacement is meter.
  • To measure a distance or displacement, the references, i.e., starting and endpoints, are required.
  • The dimension of both distance and displacement are equal, i.e., L
  • Distance and displacement can become identical for some instances, i.e., When an object is in a linear path and when a thing is in a single direction.

Therefore, distance and displacement can have some similar features.

Frequently asked questions | FAQs

Do distance and displacement are equal for an object?

The distance and displacement can be equal for a body in some specific cases.

For example, a bike moves in a straight route as long as possible in a single direction. In this case, both distance and displacement of the motorcycle can become equal.

What is the meaning of distance?

Distance is nothing but a measurable physical quantity of magnitude of objects.

The scalar quantity gives a numerical value of the length of the course of a path from beginning to end of the motion, irrespective of the direction in which the body moves. Distance never depends on the direction.

What is the meaning of displacement?

Displacement focuses on the measure of the shortest distance of a course.

It is generally defined as an example of a physical vector quantity, which gives both numerical values of shortest length and direction of a route when a body is in uniform or non-uniform motion.

What are the applications of distance and displacement?

There are many applications of distance and displacement in daily life, which are as follows;

  • The knowledge of distance and displacement is required by engineers, architects, designers while panning things.
  • It is used in the navigation of objects.
  • Locksmiths use the concept to design locks.
  • Tumbler uses it to design the length of the pipeline.
  • Every day people use the idea to estimate the path length.

How does distance differ from displacement?

Distance and displacement differ from each other in many aspects.

Distance is considered the most extended length of the course route without considering direction. It is scalar in nature, and displacement is the minimum length of the street with direction; it is a vector in nature.

Do distance and displacement measure the same thing?

Distance and displacement are entirely two different quantities.

Both distance and displacement are physical quantities. Here, distance is the measure of the longest path covered by the body, and displacement gives an estimate of the shortest route; in addition to that, it also indicates the direction of motion in which the body moves.

Raghavi Acharya

I am Raghavi Acharya, I have completed my post-graduation in physics with a specialization in the field of condensed matter physics. Having a very good understanding in Latex, gnu-plot and octave. I have always considered Physics to be a captivating area of study and I enjoy exploring the various fields of this subject. In my free time, I engage myself in digital art. My articles are aimed towards delivering the concepts of physics in a very simplified manner to the readers. Let’s connect through - LinkedIn: https://www.linkedin.com/in/raghavi-c-s-260a801b1 EMAIL ID: raghavics6@gmail.com

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